# Q & A: Can a single photon lose part of its energy?

Q:
When the photon hits a wall, can it give only part of its energy to an atom and the bounce back as less energy photon/lower frequency wave? Or as quantum it can only be fully absorbed or reflected?
- Lucas (age 31)
Poland
A:

Hi Lucas,

Single photons, just like classical beams of light, can gain or lose a bit of energy when they scatter off an object.

The simplest example of this is in the case of a moving mirror. Imagine that the mirror is moving rapidly towards the light source. When a single photon hits the mirror, it exerts some radiation pressure on the mirror, so it slows the mirror down ever-so-slightly when it bounces off. By conservation of momentum, then, the photon gains a little bit of momentum. Since momentum and wavelength are inversely related, we say the particle has undergone blueshift: its wavelength is a bit shorter than it was before bouncing off the mirror.

Even though the photon is a quantum of the electromagnetic field (and so can't be divided), its energy, momentum, and wavelength are all continuous variables, and aren't generally constrained to specific values. So, there's no problem when they gain or lose a bit of energy from scattering.

By the way, this can lead to some pretty cool effects. For example, if you bounce light off a mirror and measure the Doppler effect very carefully, you can see that it gains and loses a bit of energy from the microscopic vibrations of the mirror. So, if you plot the frequency of the light after the mirror, you'll see the light is a bit more red or more blue than the light you sent in. As above, this happens because the light gains or loses a bit of energy when the mirror is moving forward or backward, respectively.

Now, in the ground state, quantum mechanics predicts that the mirror will still have some minimum amount of motion, and some minimum amount of energy, neither of which are zero. If you cool the mirror to its ground state and then bounce light off of it, you might expect to see the red and blueshift, like before: after all, the mirror is still vibrating just a bit. However, in its ground state the mirror cannot lose any energy, so the photon can't gain any energy!

Conclusion? If quantum mechanics is correct, you should see redshift (where the light gives the mirror energy), but not blueshift (where the mirror would have to give the light energy)! This amazing effect was in fact measured recently. You can find more information in this nice video:

Awesome side note: in doing this experiment, the physicists had to measure zero-point vibrations of the mirror which were 10,000 times smaller than an atom!

Cheers,

David Schmid

(published on 11/06/2013)